题目
sin(x/3)sin(nx)dx的不定积分
提问时间：2020-11-24
答案
积化和差公式：
sin(x/3)sin(nx) = (1/2)[cos(x/3 - nx) - cos(x/3 + nx)]
∫ sin(x/3)sin(nx) dx
= (1/2)∫ cos(x/3 - nx) dx - (1/2)∫ cos(x/3 + nx) dx
= (1/2)[1/(1/3 - n)]∫ cos[(1/3 - n)x] d[(1/3 + n)x] - (1/2)[1/(1/3 + n)]∫ cos[(1/3 + n)x] d[(1/3 + n)x]
= 1/[2(1/3 - n)]sin(x/3 - nx) - 1/[2(1/3 + n)]sin(x/3 + nx) + C
= [3/(2 - 3n)]sin(x/3 - nx) - [3/(2 + 3n)]sin(x/3 + nx) + C
sin(x/3)sin(nx) = (1/2)[cos(x/3 - nx) - cos(x/3 + nx)]
∫ sin(x/3)sin(nx) dx
= (1/2)∫ cos(x/3 - nx) dx - (1/2)∫ cos(x/3 + nx) dx
= (1/2)[1/(1/3 - n)]∫ cos[(1/3 - n)x] d[(1/3 + n)x] - (1/2)[1/(1/3 + n)]∫ cos[(1/3 + n)x] d[(1/3 + n)x]
= 1/[2(1/3 - n)]sin(x/3 - nx) - 1/[2(1/3 + n)]sin(x/3 + nx) + C
= [3/(2 - 3n)]sin(x/3 - nx) - [3/(2 + 3n)]sin(x/3 + nx) + C
举一反三
我想写一篇关于奥巴马的演讲的文章,写哪一篇好呢?为什么好
奥巴马演讲不用看稿子.为什么中国领导演讲要看?
想找英语初三上学期的首字母填空练习……
英语翻译
1,人们染上烟瘾,最终因吸烟使自己丧命.
最新试题
热门考点